Some estimates of precision of the Huygens approximation

Abstract

In this paper are given some estimates of precision of the Huygens approximation $x\approx \frac{2}{3}\sin x+\frac{1}{3}\tan x,$ for right neighbourhood of zero, by determining some boundaries for the Huygens function $f(x)=\frac{2}{3}\sin x+\frac{1}{3}\tan x,$ for $x\in \left(0,\frac{\pi }{2}\right)$, in forms of some polynomial and some rational functions.

This article is included in one new extended article B. Malesevic, M. Nenezic, L. Zhu, B. Banjac, M. Petrovic: Some new estimates of precision of Cusa-Huygens and Huygens approximations (arXiv:1907.00712)